Solve -7x^5(2x^2)^3/4x^2

$$\frac { - 7 x ^ { 5 } ( 2 x ^ { 2 } ) ^ { 3 } } { 4 x ^ { 2 } }$$

Evaluate

$$-14x^{9}$$

Solution Steps

Cancel out x^{2} in both numerator and denominator.

$$\frac{-7x^{3}\times \left(2x^{2}\right)^{3}}{4}$$

Expand \left(2x^{2}\right)^{3}.

$$\frac{-7x^{3}\times 2^{3}\left(x^{2}\right)^{3}}{4}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{-7x^{3}\times 2^{3}x^{6}}{4}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-7x^{3}\times 8x^{6}}{4}$$

Multiply -7 and 8 to get -56.

$$\frac{-56x^{3}x^{6}}{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$\frac{-56x^{9}}{4}$$

Divide -56x^{9} by 4 to get -14x^{9}.

$$-14x^{9}$$

Expand

$$-14x^{9}$$

Solution Steps

Cancel out x^{2} in both numerator and denominator.

$$\frac{-7x^{3}\times \left(2x^{2}\right)^{3}}{4}$$

Expand \left(2x^{2}\right)^{3}.

$$\frac{-7x^{3}\times 2^{3}\left(x^{2}\right)^{3}}{4}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{-7x^{3}\times 2^{3}x^{6}}{4}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-7x^{3}\times 8x^{6}}{4}$$

Multiply -7 and 8 to get -56.

$$\frac{-56x^{3}x^{6}}{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$\frac{-56x^{9}}{4}$$

Divide -56x^{9} by 4 to get -14x^{9}.

$$-14x^{9}$$